Given that, in momentum space, it is well known that Poincaré symmetry uniquely fixes the three-point function between massless particles up to an overall coupling coefficient, our findings are not entirely surprising. These three-point functions are directly related to the tree-level collinear splitting functions. Poincaré symmetry is therefore sufficient at tree-level to fix leading celestial OPE coefficients simply because these coefficients are the image of the splitting functions under a transformation to a boost weight basis. Nevertheless, a precise implementation of this argument was hitherto muddled, in part due to the singular nature of the three-point functions in boost-weight space [1]}.Boost-eigenstates of massless particles constructed with an additional light transformation were recently shown to admit smooth three-point functions, which are more directly related to the OPE coefficients [2]}.
